Do I have to pay for the full month or only for the days in the month until 30 days notice is reached?

Assuming your rent is due on the 1st and you pay rent in advance, Your notice in the middle of November becomes effective Dec. 1st for a Dec. 31st lease termination. On Dec. 1st you will be required to pay December's full rent and you will have until the end of the month to move. However, if you have already found a place and you wish to move earlier, coordinate with your landlord. It is possible he or she will give you a prorated refund of December rent if another tenant moves in some time before month's end. Good luck!